If a,b,c are xth,yth,zth terms of a GP respectively then

(y - z) loga + (z - x) logb + (x - y) logc is?

Asked by Topperlearning User | 25th Sep, 2017, 12:01: PM

Expert Answer:

straight a equals AR to the power of straight x minus 1 end exponent
straight b equals AR to the power of straight y minus 1 end exponent
straight c equals AR to the power of straight z minus 1 end exponent
where space straight A space and space straight R space are space first space term space and space common space ratio space respectively.
loga equals logA plus left parenthesis straight x minus 1 right parenthesis logR
logb equals logA plus left parenthesis straight y minus 1 right parenthesis logR
logc equals logA plus left parenthesis straight z minus 1 right parenthesis logR
left parenthesis straight y minus straight z right parenthesis space loga plus left parenthesis straight z minus straight x right parenthesis space logb plus left parenthesis straight x minus straight y right parenthesis space logc equals left parenthesis straight y minus straight z plus straight z minus straight x plus straight x minus straight y right parenthesis space logA space plus space left curly bracket left parenthesis straight y minus straight z right parenthesis left parenthesis straight x minus 1 right parenthesis space plus space left parenthesis straight z minus straight x right parenthesis left parenthesis straight y minus 1 right parenthesis space plus space left parenthesis straight x minus straight y right parenthesis left parenthesis straight z minus 1 right parenthesis right curly bracket space logR
0 logA plus 0 logR equals 0

Answered by  | 25th Sep, 2017, 02:01: PM